Question

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Answer 1

       

Here, AD² = AB² - BD²

And CD = BC - BD

ΔADC is also a right triangle.

∴ AC² = AD² + CD²

⇒ AC² = (AB² - BD²) + (BC - BD)²

⇒ AC² = AB² - BD² + (BC² - 2BC × BD + BD²)

⇒ AC² = AB² - BD² + BC² - 2BC × BD + BD²

⇒ AC² = AB² + BC² - 2BC × BD

Hence proved!!!

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